| | I wrote: "Each thing that exists cannot be caused by another thing, because that implies an infinite regress." Craig replied: What do you have against infinite regress? I've been trying to battle that particular antipathy for some time now. It's quite widespread, among people that otherwise don't agree on much.
Seriously, what do you (and Warren, if he's still watching) object to in an infinity, either of causes, or of space or time? The problem with an infinite regress of causes is that it is generated by a contradiction. So, you say that every thing must have a cause, which means that everything is the effect of something else. But everything cannot be the effect of something else, because you cannot have something else in addition to everything. Everything is all that exists; hence the contradiction. The infinite regress comes from tracing out the implications of the contradiction: Viz., everything has a cause; since the cause is something, it too must have a cause, and since its cause is something, it too must have cause, etc., ad infinitum. The only way to resolve the regress is to recognize that a cause requires an existent; an existent (as such) does not require a cause.
As for other kinds of infinity: The universe (defined as everything that exists) cannot be spatially infinite, because in order for a three-dimensional object to exist, it must be something specific, which means that it must have a specific size and shape, and therefore be limited in the extent of its dimensions. By the same token, the number of existents, however you define "existent," also cannot be infinite, because whatever the number is, it must be some specific number, however large.
Nor can the universe be temporally infinite, because time depends on motion, and motion involves a relationship between at least two objects. Therefore, since motion cannot apply to the universe as a whole, because nothing exists outside the universe, time does not apply to the universe as a whole. Therefore, the universe does not have a temporal duration, and cannot therefore be infinite in time. One could say that the universe is "eternal," if by "eternal," one simply means timeless or outside of time, which is the original meaning of the term.
The series of natural numbers is potentially infinite in the sense that however far you count, there is no metaphysical limitation on counting further. But no arithmetical series is actually infinite, because however far you count, you will always be at some finite number.
- Bill
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